Theorem 3orel13

Description: Elimination of two disjuncts in a triple disjunction. (Contributed by Scott Fenton, 9-Jun-2011)

	Ref	Expression
Assertion	3orel13	$$⊢\left(\neg \phi \wedge \neg \chi \right)\to \left(\left(\phi \vee \psi \vee \chi \right)\to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		3orel3	$$⊢\neg \chi \to \left(\left(\phi \vee \psi \vee \chi \right)\to \left(\phi \vee \psi \right)\right)$$
2		orel1	$$⊢\neg \phi \to \left(\left(\phi \vee \psi \right)\to \psi \right)$$
3	1 2	sylan9r	$$⊢\left(\neg \phi \wedge \neg \chi \right)\to \left(\left(\phi \vee \psi \vee \chi \right)\to \psi \right)$$